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Application of the mixed formulation method to eliminate shear-locking phenomenon in the Peridynamic Mindlin plate model

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Accurately predicting crack propagation in structures remains a key challenge within the finite element method (FEM) framework. Despite developing the local method to mitigate the challenges encountered in the FEM, this method is computationally demanding and inadequate for accurately modeling fracture processes in actual structures. Recently, a powerful nonlocal method, Peridynamics (PD), has been proposed by employing integral equations rather than differential equations to address various discontinuous problems. This study introduces the classical Peridynamic Mindlin plate theory (classical PD) to characterize the kinematics of thick plates. However, the application of the classical PD to extremely thin plate structures results in a shear-locking phenomenon, causing inaccuracies in the solutions. Although the reduced integration with a single-point rule provides an alternative solution to address the shear-locking problem, its sensitivity to the point number in the horizon becomes especially pronounced in the case of discontinuities. To ensure stability and broad applicability, this paper presents a more general mixed formulation method (mixed PD) that can yield accurate results ranging from very thick to thin plate configurations. The efficacy of the mixed PD is demonstrated via several numerical cases.

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Acknowledgements

This research is funded by the Entrepreneurship and Innovation Support Program for Chongqing Overseas Returnees (cx2023003), Key Project of Chongqing Natural Science Foundation (cstc2020jcyj-zdxmX0014), Shuguang Program (18SG36), National Natural Science Foundation of China (62303079, 52105244, 62103065), and Fundamental Research Funds for the Central Universities (2023CDJXY-014, 02090052020106).

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Authors and Affiliations

  1. State Key Laboratory of Mechanical Transmission for Advanced Equipment, Chongqing University, Chongqing, 400044, China

    Ruqing Bai, Jinglei Zhao, Jin Yi, Xueping Li, Shujin Yuan, Jun Luo, Liming Wang & Huayan Pu

  2. INSA Hauts-de-France, CNRS UMR 8201-LAMIH, 59313, Valenciennes, France

    Hakim Naceur

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  1. Ruqing Bai
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All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Ruqing Bai and Hakim Naceur. The first draft of the manuscript was written by Ruqing Bai and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Hakim Naceur or Huayan Pu.

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Bai, R., Naceur, H., Zhao, J. et al. Application of the mixed formulation method to eliminate shear-locking phenomenon in the Peridynamic Mindlin plate model. Comp. Part. Mech. (2023). https://doi.org/10.1007/s40571-023-00677-9

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